Hi!
While the question is definitely interesting I would put the answer in different terms.
When looking at reconstructing the text from a vector it is a comparison to a (de-)compression method and not a transformation into a semantic representation of the meaning. And while vector embeddings have been around for a while I am not aware of any archiving app that uses vectors to compress text. This is a good hint that the task is definitely not trivial.
Next, yes, training data and even the complete model with weights and parameters and whatnot are available in the open source space. Thus, yes, researchers have tried to recreate the embedded text for example using AI models trained especially for this task. They wrote nice and somewhat intriguing papers but these approaches come with a lot of strings attached which leads to results like “in theory it should be possible”.
But from the perspective of practically developing actual apps that make use of such a technology the answer is a lot closer to a hard “no”.
You can take a look at this previous discussion where the intricacies are spelled out in more detail: